Definition 2.3 (see [1]}) An object \(P\in \mathcal {C}\)  is called \(\xi \) -projective if for any triangle \({A[r]& B[r]& C [r]& \Sigma A}\)  in \(\xi \) , the induced sequence of abelian groups
\({0[r]& \mathcal {C}(P,A)[r]& \mathcal {C}(P,B)[r]&\mathcal {C}(P,C)[r]& 0}\) 
